I concur 100% with the preceding posts.
In addition to the other negative factors mentioned for studded tires, you should be aware that the studs will wear out in ~10k miles.
Modern winter tires (the term “snow tires” represents outdated technology) on all 4 wheels will allow you to get through virtually any winter road conditions, and as previously mentioned, will allow your ABS and stability control system to work at their optimum. Having mis-matched tires will “confuse” these systems.
I strongly recommend the Michelin X-Ice winter tires, but virtually any winter tire (with the snow flake/mountain peak symbol on the sidewall) will give you an incredible increase in winter traction as compared to so-called all-season tires.